Question

Four numbers whose sum is 40 and sum of their squares is 480. What are the four numbers?

(a) 4, 8, 12, and -16

(b) 4, 8, 12, and 16

(c) -4, 8, 12, and 16

(d) 4, -8, 12, and 16

The question was asked during an online interview.

Asked question is from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10

Answer 1

Right choice is (b) 4, 8, 12, and 16

To elaborate: Let the four numbers be (a + 3d), (a + d), (a – 3d), (a – d).

Sum of the four numbers is 40.

a + 3d + a + d + a – 3d + a – d = 40

4a = 40

a = 10

Sum of their squares is 480.

(a + 3d)^2 + (a + d)^2 + (a – 3d)^2 + (a – d)^2 = 480

4a^2 + 20d^2 = 480

10^2 + 5d^2 = 120

100 + 5d^2 = 120

5d^2 = 20

d^2 = 4

d = 2, -2

Hence the four numbers are 4, 8, 12, and 16.